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arXiv 2011.10546eess.SP
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FIR滤波器设计中一种基于切比雪夫多项式的sinc函数替代函数

A Function Based on Chebyshev Polynomials as an Alternative to the Sinc Function in FIR Filter Design

Paul W. Oxby

备注：
28 pages, 6 figures, 10 tables. This revision retracts the erroneous last two paragraphs of Section 8. A detailed discussion of the anomalous result illustrated in Figure 6.3 is presented in Appendix 3. The proof of the convergence of the sinc function and the alternative to the sinc function in Section 2 has been replaced with a simpler proof
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AI总结：

针对截断sinc函数设计FIR滤波器时通带存在吉布斯波纹的问题，提出基于切比雪夫多项式的替代函数，其傅里叶变换通带单调递减，且自带可调参数的内置窗函数以调控过渡带和阻带特性。

摘要：

sinc函数常被用作离散线性相位FIR滤波器设计的基础。然而，受吉布斯现象影响，截断sinc函数的傅里叶变换在通带内存在波纹。本文提出一种基于切比雪夫多项式的替代函数，其傅里叶变换在通带内单调递减。此外，该函数自带一个内置窗函数，该窗函数带有一个可调参数，可影响过渡带和阻带内的傅里叶变换特性。

英文摘要：

The sinc function is often used as the basis for the design of discrete linear-phase FIR filters. However the Fourier transform of the truncated sinc function exhibits ripple in the pass band due to the Gibbs phenomenon. This paper introduces an alternative function based on Chebyshev polynomials whose Fourier transform decreases monotonically in the pass band. Furthermore this function features an intrinsic window function with an adjustable parameter influencing the Fourier transform in the transition and stop bands.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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